International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. F. ch. 22.1, p. 537   | 1 | 2 |

Figure 22.1.1.8 

M. Gersteina* and F. M. Richardsa
[Figure 22.1.1.8]
Figure 22.1.1.8

Packing efficiency. (a) The relationship between Voronoi polyhedra and packing efficiency. Packing efficiency is defined as the volume of an object as a fraction of the space that it occupies. (It is also known as the `packing coefficient' or `packing density'.) In the context of molecular structure, it is measured by the ratio of the VDW volume ([V_{\rm VDW}], shown by a light grey line) and Voronoi volume ([V_{\rm Vor}], shown by a dotted line). This calculation gives absolute packing efficiencies. In practice, one usually measures a relative efficiency, relative to the atom in a reference state: [(V_{\rm VDW}/V_{\rm Vor})/[V_{\rm VDW}/V_{\rm Vor}\hbox{(ref)}]]. Note that in this ratio the unchanging VDW volume of an atom cancels out, leaving one with just a ratio of two Voronoi volumes. Perhaps more usefully, when one is trying to evaluate the packing efficiency P at an interface, one computes [P = p \textstyle\sum\displaystyle V_{i}/\textstyle\sum\displaystyle v_{i}], where p is packing efficiency of the reference data set (usually 0.74), [V_{i}] is the actual measured volume of each atom i at the interface and [v_{i}] is the reference volume corresponding to the type of atom i. (b) A graphical illustration of the difference between tight packing and loose packing. Frames from a simulation are shown for liquid water (left) and for liquid argon, a simple liquid (right). Owing to its hydrogen bonds, water is much less tightly packed than argon (packing efficiency of 0.35 versus ∼0.7). Each water molecule has only four to five nearest neighbours while each argon atom has about ten.